There is a term used to describe something which might otherwise be classifiable as a "mint error", but which isn't literally an "error" because it was deliberately made: a "mint sport". A mint sport is what it says on the box: someone inside the mint having some fun, using mint equipment in an unauthorized (and probably not entirely safe) fashion to create non-usual-looking coins.
Mint sports are nevertheless a subcategory of "mint errors", simply because such an object cannot preserve the "intent" of the person doing it. Most "mules", for example, are honest mistakes: someone in the Mint accidentally inserted the wrong working die into the press, and no-one noticed until after a few thousand coins were already struck. But it's also entirely possible for a mint worker to deliberately insert the wrong die, and cause some mules to be made. You can't really tell the "mint error mules" and the "mint sport mules" apart just by examining the coins; you need to examine the context in which the coins were found and make some educated guesses or assumptions. Were they found all mixed up amongst the coins issued for general circulation? Then they're probably accidents and thus "errors". Were they found on the person of a mint worker trying to smuggle them out of the mint, or every single known example just happened to end up in the possession of the exact same coin dealer? Then they're "sports".
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis